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Double-Anonymous Peer Review in Mathematics: Implementation for American Mathematical Society Journals

Dan Abramovich
Henry Cohn
David Futer
Robert Harington

In March 2022, the American Mathematical Society (AMS) launched double-anonymous peer review across its journal program, beginning with Proceedings of the American Mathematical Society and Representation Theory. In February 2024 implementation expanded to the Transactions and Memoirs of the American Mathematical Society. Further rollout across AMS journals is ongoing. The goal of the double-anonymous peer review policy is to reduce implicit bias in peer review, including bias along gender, racial, and geographical lines, along with seniority bias.

Peer review in mathematics has traditionally centered on single-anonymous peer review. In this model, reviewers are aware of the identities of an article’s author(s), but the reviewer(s) remain anonymous to authors. In double-anonymous peer review (formerly known as double-blind), both reviewers and authors are anonymous to each other.

Peer review is central to scholarship and is deployed across all academic disciplines. As Melinda Baldwin discusses in her excellent article 2 (see similar discussion in 1):

The most widely accepted story about peer review’s origin credits Henry Oldenburg with inventing it for the seventeenth-century Philosophical Transactions of the Royal Society, creating the impression that refereeing has been an unchanging part of science for over three hundred years. However, new historical work is beginning to shed more light on peer review’s development—and the real story is far more complicated than the neat tale of Oldenburg inventing refereeing out of whole cloth during the Scientific Revolution.

Most existing histories of peer review have focused on the emergence of the scientific referee during the nineteenth century or on the inner workings of referee systems at particular journals. Those studies have shown that refereeing was not initially thought of as a process that bestowed scientific credibility and that many high-profile journals and grant organizations had unsystematic (or nonexistent) refereeing processes well into the twentieth century.

Across much of the social sciences and humanities, double-anonymous peer review is the standard system of peer review. It is also becoming increasingly common in the natural sciences. In physics, the Institute of Physics Publishing (IOPP) launched double-anonymous peer review across all of its sixty-one journals in 2021 3. In astronomy, NASA practices double-anonymous peer review in its grant applications. In certain subdisciplines of computer science, including cryptography, double-anonymous peer review is quite common.

Why did the AMS move to implement double-anonymous peer review across its journals? The motivation for the AMS Council to adopt this change is so the referee’s first impressions of a paper are not dominated by its list of authors and their affiliations. Instead, double-anonymous refereeing aims to focus attention on the mathematics. It may still be possible to infer who wrote a submission, but it is hoped that double-anonymity lowers the likelihood of implicit bias and therefore supports inclusivity and diversity across mathematics.

The AMS Council approved the transition to double-anonymous peer review as a policy in January 2021. The AMS President, Ruth Charney, subsequently formed the Double-Anonymous Refereeing Committee, on which we served, charged with discussing how an implementation could work. During implementation discussions, it became clear that in mathematics, this form of peer review needed to be implemented with a light touch. While authors are required to submit manuscripts without author names or affiliations, they are not required to anonymize references, acknowledgments, or funding information, or to make other edits. Journal editors continue to have access to author and reviewer identities in double-anonymous peer review. In particular, editors can use this information in order to avoid conflicts of interest.

The new policy is guided by the AMS’s strong belief in open dissemination of mathematics. There are no new restrictions on how authors choose to disseminate and publicize their work—for example, by giving talks, posting preprints that include author names, and discussing with colleagues.

Referees are asked not to go out of their way to try to identify authors, but the AMS policy accepts that referees will sometimes already know who wrote the submission. For instance, a referee may already know the paper if they have seen it posted to the arXiv preprint server. Even in those cases, double-anonymous refereeing is a statement of principle about how submissions should be evaluated.

Authors submitting articles to AMS journals employing double-anonymous peer review are tasked with the following tasks that represent a light touch to double-anonymous peer review.

At article submission, authors are asked to submit a version which does not include their names or affiliations in the preamble, headers, or footnotes of the paper. Authors may also choose to reword other instances in the paper that would tend to identify them, but this is not required. For example, a phrase like “we showed” or “the second author showed” could be replaced by “Smith showed,” referring to the author in the third person. If a paper is accepted, such wording can be adjusted prior to publication. At initial submission, AMS staff screens for author names in the paper itself, in the running heads, and in the affiliations list.

A typical communication used in requests and reminders typically reads: “The PDF must not contain any information that can identify the author(s). In particular, there must be no authors’ names nor authors’ affiliations/email addresses listed in the paper, nor any links to their identities in any way.” In addition, identifiable versions are never released to referees.

Implementation of this light-touch approach to double-anonymous peer review is underway. As the AMS rolls this peer review model out across the journal portfolio, it is important to gather data and assess the effects of double-anonymous peer review on authors, reviewers, and editors.

The AMS is in the early stages of developing an organization-wide approach to demographic data collection for both our membership and publishing/research communities. In order to monitor the existence of many types of bias in our research community this data will need to be collected both at submission of a manuscript and post decision. In the meantime, we can choose to look at geographical data and institutional data.

The data to be collected will help the AMS see to what extent the goals of the policy are achieved. But, first and foremost, we need to know that no serious harm is done. Concerns raised by journal editors included: (i) Will people continue to agree to provide expert opinions and write detailed referee reports? (ii) Will authors continue to submit papers appropriate to the journal’s portfolio? (iii) Will colleagues continue to agree to serve as editors? A previous introduction of a double-anonymous policy in 1975 was abandoned in 1980 on these counts 4.

After double-anonymous peer review was rolled out to Proceedings and Representation Theory, we were able to examine the first two of these concerns.

Both Proceedings and Representation Theory transitioned to double-anonymous peer review in 2022. As illustrated in Figure 1, double-anonymous peer review does not seem to have had any impact that sets them apart from our other journals.

Figure 2 is a preliminary look at reviewer denial data for the two AMS journals utilizing double-anonymous peer review, versus all other AMS journals.

Figure 1.
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Figure 2.
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This data indicates that reviewers are not turning down an opportunity to review for the AMS due to journals embracing double-anonymous peer review.

For the third concern (editors’ willingness to serve), the data sample is too small to conduct statistics. Suffice it to say that the AMS Editorial Boards Committee did not face difficulties in filling editorial vacancies in the two journals in which the policy was implemented.

References

[1]
Melinda Baldwin, In referees we trust?, Physics Today 70 (2017), no. 2, DOI 10.1063/PT.3.3463.,
Show rawAMSref \bib{phys}{article}{ author={Baldwin, Melinda}, title={In referees we trust?}, journal={Physics Today}, volume={70}, number={2}, date={2017}, doi={10.1063/PT.3.3463}, }
[2]
Melinda Baldwin, Scientific Autonomy, Public Accountability, and the Rise of “Peer Review” in the Cold War United States, Isis 109 (2018), no. 3, DOI 10.1086/700070.,
Show rawAMSref \bib{isis}{article}{ author={Baldwin, Melinda}, title={Scientific Autonomy, Public Accountability, and the Rise of ``Peer Review'' in the Cold War United States}, journal={Isis}, volume={109}, number={3}, date={2018}, doi={10.1086/700070}, }
[3]
Rachael Harper, IOP Publishing commits to adopting double-anonymous peer review for all journals (2020).,
Show rawAMSref \bib{iopp}{article}{ author={Harper, Rachael}, title={IOP Publishing commits to adopting double-anonymous peer review for all journals}, date={2020}, url={https://ioppublishing.org/news/iop-publishing-commits-to-adopting-double-blind-peer-review-for-all-journals/}, }
[4]
Everett Pitcher, A history of the second fifty years, American Mathematical Society, 1939–1988, Vol. I, American Mathematical Society, Providence, RI, 1988, DOI 10.1007/bf01017168. MR1002190,
Show rawAMSref \bib{pitcher}{book}{ author={Pitcher, Everett}, volume={I}, title={A history of the second fifty years, American Mathematical Society, 1939--1988}, publisher={American Mathematical Society, Providence, RI}, date={1988}, pages={viii+346}, isbn={0-8218-0125-2}, review={\MR {1002190}}, doi={10.1007/bf01017168}, }

Credits

Figures 1 and 2 are courtesy of the AMS.

Photo of Dan Abramovich is courtesy of Deidre Confar.

Photo of Henry Cohn is courtesy of MFO. CC BY-Sa 2.0 DE.

Photo of David Futer is courtesy of the AMS.

Photo of Robert Harington is courtesy of the AMS.